Notes from Bertrand Russell's History of Western Philosophy, in particular the sections on ancient philosophy and theology.

• Western civilisation began in the city-states of Greece - and there wasn't any comparable intellectual and artistic flourishing until the city-states of Italy during the Renaissance. Russell argues that this isn't a coincidence: that the intellectual climate of a time is bound up in the political and historical circumstances.
• He also draws several dichotomies: between optimistic and pessimistic times; between individualistic and grouped times; also systematic and piecemeal; also subjective and objective. Some of these are useful perspectives, although they're the sort of categories we should be careful not to over-generalise.
• Russell holds that the first philosophers created scientific hypotheses which were, if not exactly testable, at least empirically meaningful. These included Thales (around 585 BC; he held that everything was made out of water) and his Milesian School, Anaximander (everything was made of one elemental substance), Anaximenes (air), Heraclitus (fire and change), Parmenides (no change), Empedocles (4 elements), Anaxagoras (infinite divisibility) and eventually Democritus (atoms), who was perhaps the most rigorous, though his correctness was still essentially accidental. These were also, notably, all reductionist doctrines, in that they were concerned with analysing objects in terms of their simpler components; and non-teleological (although Anaximander incorporated a notion of cosmic "justice").
• We must also include Pythagoras as the founder of mathematics (in the sense of demonstrative deductive arguments), whose influence is a source of the belief in "eternal and exact truth" in philosophy. He forwarded a view of philosophers as contemplative gentleman aristocrats, and foreshadowed Plato's forms.
• Next, the Sophists, led by Protagoras, who claimed the skeptical hypothesis that "[each] man is the measure of all things."
• After this, we encounter Socrates, Pluto and Aristotle, the three greatest names in ancient philosophy but also (along with Protagoras) heralds of a turn towards human-centred philosophy. Socrates, insofar as we can separate him from Plato, was largely concerned with ethical questions, which he approached using the Socratic method of conceptual analysis, which teased out details of what people generally agreed were virtues.
• Plato is best known for his political philosophy, metaphysics and theology. Unfortunately, all were pernicious influences on the next two millennia of intellectual thought. His ideal Republic was based on the myth of Sparta, and essentially totalitarian (based, again, on "justice" as occupying one's natural role) Indeed, it is not surprising that he embraced a unilateral conception of the good, since it is implicit in his doctrine of forms. This metaphysic is not just false but deeply anti-empirical and anti-reductionist. So is his identification of a universal and perfect God.
• Aristotle was unfortunately similarly theological. Known in the medieval period simply as "The Philosopher", he came up with a competing theory to Pluto's forms, as well as the idea of logical syllogisms. Everything above the moon was indestructible and eternal. The ultimate source of all movement was Will; God's existence could be proved by identifying him as the First Mover. Metaphysics was essentially frozen at this point for two millennia. Aristotle's account of causes was largely teleological; his ethics (particularly the "golden mean") absolutist. Notably, the best individual would be a "proud, great-souled" man who knows his own greatness - in stark contrast to Christianity. Similarly to Plato, this implies an identification of ethics as intrinsically political, because the rest must be subordinate to such great men. The supreme pleasure is contemplation. The aim of the state is to produced cultured gentlemen, such as those of the Athens of Pericles, or the 18th century - but their day is past.
• Russell argues that many of the errors made in Plato can be corrected using a system of predicate logic - for example, his misunderstanding of relational propositions, and his claims that something can be "one" (or other numbers).
• After the Alexandrean conquests, the Greek world became chaotic, and philosophers became more specialised, as well as superstitious. Ethics becomes of foremost importance, as men strove to deal with the general confusion - in particular by cultivating mindsets that would help endure the suffering of life, rather than those that would promote any energetic or useful activity.
• The Cynics, led by Diogenes, taught that we should reject worldly goods and instead focus on virtue. This passed into Zeno's Stoicism, which argued that such pursuit of virtue was independent of all external circumstances. Stoicism greatly influenced a number of Romans, notably Seneca, Epictetus and Marcus Aurelius.
• By contrast, Epicurus considered pleasure and the avoidance of pain to be the good. Virtue is "Prudence in the pursuit of pleasure" - like the Stoics, he thought attitude incredibly important and argued that, in practice, most desires and extreme pleasures led to more pain than they were worth. Epicurus thought that "death was nothing to us", and religions should be overthrown, since the supernatural causes terror. 
• Meanwhile Pyrrho, the Sceptic, denied the ability to know anything, and concluded that we should fall back on common practice.
• These doctrines were all more universal than those of previous philosophers - Rome was the world, and thus it was easy to believe in one universal culture and brotherhood. As Rome declined, Plotinus forwarded Neoplatonism, an important precursor to Christian theology in its focus on another more perfect world, accessed by looking inwards and reflecting.
• The Church also contained important elements from Judaism - in particular, a sacred history; an identity as God's chosen few; a conception of righteousness; the Messiah and the Kingdom of Heaven. Jews distinguished themselves by their monotheism, and the wickedness of all other religions. This meant that their suffering could only be explained by the sins of the Jewish people in violating their laws. This made them particularly rigid - during the Maccabean Revolt, many Jews were tortured and killed for refusing to eat pork or stop circumcising their children.
• Gibbons identifies five factors behind Christianity's rise:
1. Inflexible religious zeal
2. Doctrine of future life
3. A sacred book which testified to a miraculous history
4. Pure and austere morality
5. Union and discipline of Christian organisation
• Doctrinal rigidity caused a number of conflicts over heresies, the most notable being the Arian heresy that God the Father was superior to Jesus. This was condemned at the Council of Nicaea in 325, which (along with Constantine's acceptance of Christianity) heralds a doctrinal consolidation and the end of the early Christian period. It's notable how many of the early heresies made almost entirely opposite claims to other heresies, with only a narrow middle ground being acceptable (e.g. the Nestorian and Monophysite heresies; the Arian and Sabellian hereises).
• The "four doctors of the Church" from the 4th to 6th centuries were St Ambrose, St Jerome, St Augustine and Pope Gregory the Great. The first initiated the consolidation of power in the Papacy, the second translated the Bible and was a major influence towards monasticism, and the third was the foundation of Catholic theology. Augustine was obsessed by sin: passed down from Adam, God redeems some of us from it via predestination, although none of us deserve redemption. He holds that the Church must be separate from and superior to the State. He is heavily Platonic. Around this time an intense admiration for celibacy developed, and it became essential for the moral authority of the church. Gregory the Great is known for instigating the Gregorian Mission to convert the Anglo-Saxons, as well as his prolific writings.
• St Benedict founded the most important monastic group, the Benedictine Order, at the beginning of the 6th century. Benedictines did not have to be as austere as previous monks. Around this time Gregory the Great was consolidating power in the papacy, Justinian was compiling Roman law - and Muhammed was born. Thus the men of the 6th century had a disproportionate influence on the world. However, the Dark Ages over the next 5 centuries meant very little intellectual progress occurred. In the 11th century, St Anselm laid out the ontological argument for God. From around then on, ancient philosophy began to be rediscovered, mainly via Islamic scholars.
• By the 13th century, the popes had lost much of their moral authority, and a number of heretical movements sprouted. However, the rise of the mendicant orders restored some of this faith. St Francis was notably zealous in his austerity; St Dominic similarly zealous in combating heresy. Though their orders were soon corrupted, they contained a number of philosophers, most notably Thomas Aquinas, who was a keen Aristotelian.

I also made a rough diagram of the flow of intellectual influence through the ages - again focusing on ancient philosophers, but with a few modern ones thrown in when there was a particularly strong link. Philosophers most associated with one big idea or virtue have it noted beneath them. The graph is surprisingly neat (and planar!), no doubt because I've simplified a lot of relationships and overlooked many more - don't interpret this as anything more than an outline.